0.99999999.......
       |           

Welcome, Guest. Please login or register.
Did you miss your activation email?
March 28, 2024, 05:14:11 AM
News: Election Simulator 2.0 Released. Senate/Gubernatorial maps, proportional electoral votes, and more - Read more

  Talk Elections
  General Discussion
  Religion & Philosophy (Moderator: World politics is up Schmitt creek)
  0.99999999.......
« previous next »
Pages: [1] 2 3 4
Poll
Question: Does it equal 1?
#1
Yes
 
#2
No
 
Show Pie Chart
Partisan results

Total Voters: 55

Author Topic: 0.99999999.......  (Read 20360 times)
they don't love you like i love you
BRTD
Atlas Prophet
*****
Posts: 112,693
Ukraine


Political Matrix
E: -6.50, S: -6.67

P P
Show only this user's posts in this thread
« on: November 09, 2009, 09:44:28 PM »
« edited: November 09, 2009, 09:58:37 PM by the purple mountains beneath the orange sky »

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.
Logged
Хahar 🤔
Xahar
Atlas Legend
*****
Posts: 41,731
Bangladesh


Political Matrix
E: -6.77, S: 0.61

WWW Show only this user's posts in this thread
« Reply #1 on: November 09, 2009, 09:58:15 PM »
« Edited: November 09, 2009, 10:28:19 PM by Хahar »

Yes, but voted no in response to the original question.
Logged
Associate Justice PiT
PiT (The Physicist)
Atlas Politician
Atlas Superstar
*****
Posts: 31,135
United States


Show only this user's posts in this thread
« Reply #2 on: November 09, 2009, 10:37:35 PM »

     Yes. As BRTD said, the math behind it is pretty clear-cut.
Logged
A18
Atlas Star
*****
Posts: 23,794
Political Matrix
E: 9.23, S: -6.35

Show only this user's posts in this thread
« Reply #3 on: November 09, 2009, 10:39:19 PM »

Only if one assumes that 9.99999... refers to a real number, no?
Logged
Swing low, sweet chariot. Comin' for to carry me home.
jmfcst
Atlas Icon
*****
Posts: 18,212
United States


Show only this user's posts in this thread
« Reply #4 on: November 09, 2009, 11:15:43 PM »

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

I see you have been peeking in my son's 6th grade math book.
Logged
Vepres
Junior Chimp
*****
Posts: 8,032
United States
Show only this user's posts in this thread
« Reply #5 on: November 09, 2009, 11:37:40 PM »

Sure, technically, but as it's impossible to imagine infinity, it is counter intuitive.
Logged
Swing low, sweet chariot. Comin' for to carry me home.
jmfcst
Atlas Icon
*****
Posts: 18,212
United States


Show only this user's posts in this thread
« Reply #6 on: November 09, 2009, 11:55:34 PM »

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

also, in the real world of business (e.g. floating point computations), attempting to apply simple rules of algebra will lead to the wrong answer.  Example:

x(a+b) = xa + xb in your classroom, but in the world of computer calculations, this does NOT hold true.  In fact, in the world floating points, it rarely holds true.
Logged
Obnoxiously Slutty Girly Girl
Libertas
Atlas Icon
*****
Posts: 14,899
Finland


Show only this user's posts in this thread
« Reply #7 on: November 10, 2009, 03:32:25 AM »

This is religion and philosophy? Mathematics is not a religion, but I'm sure everyone is impressed at what you learned in school today.
Logged
ChrisJG777
Jr. Member
***
Posts: 920
United Kingdom


Political Matrix
E: -5.42, S: -8.00

Show only this user's posts in this thread
« Reply #8 on: November 10, 2009, 07:48:59 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.
Logged
Franzl
Atlas Star
*****
Posts: 22,254
Germany


Show only this user's posts in this thread
« Reply #9 on: November 10, 2009, 08:07:15 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.
Logged
ChrisJG777
Jr. Member
***
Posts: 920
United Kingdom


Political Matrix
E: -5.42, S: -8.00

Show only this user's posts in this thread
« Reply #10 on: November 10, 2009, 08:13:33 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.
Logged
Franzl
Atlas Star
*****
Posts: 22,254
Germany


Show only this user's posts in this thread
« Reply #11 on: November 10, 2009, 08:28:33 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it? Smiley

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis Smiley
Logged
ChrisJG777
Jr. Member
***
Posts: 920
United Kingdom


Political Matrix
E: -5.42, S: -8.00

Show only this user's posts in this thread
« Reply #12 on: November 10, 2009, 08:41:05 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it? Smiley

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis Smiley

Still, 0.9999999... is not equal to 1.  Tongue
Logged
Franzl
Atlas Star
*****
Posts: 22,254
Germany


Show only this user's posts in this thread
« Reply #13 on: November 10, 2009, 08:49:50 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it? Smiley

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis Smiley

Still, 0.9999999... is not equal to 1.  Tongue

It is though Smiley

What's the difference between 0.9 and 1?
What's the difference between 0.99 and 1?
What's the difference between 0.999999999999 and 1?

If you truly assume an infinite number of 9s behind the decimal point....there can't be any difference between the two numbers.

To claim that the two numbers are not equal, you would have to assume a finite number of 9s behind the decimal point. But even 0.99999999999999999999999999999999999999999999 (and a million more 9s) is not equal to "0.99....".
Logged
Swing low, sweet chariot. Comin' for to carry me home.
jmfcst
Atlas Icon
*****
Posts: 18,212
United States


Show only this user's posts in this thread
« Reply #14 on: November 10, 2009, 09:30:50 AM »

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

also, in the real world of business (e.g. floating point computations), attempting to apply simple rules of algebra will lead to the wrong answer.  Example:

x(a+b) = xa + xb in your classroom, but in the world of computer calculations, this does NOT hold true.  In fact, in the world floating points, it rarely holds true.

if you're interested, here is a quick overview of the why simple math principles fall apart when coded in floating point calculations:

http://www.cs.fsu.edu/~engelen/courses/HPC-adv/FP.pdf

Logged
Obnoxiously Slutty Girly Girl
Libertas
Atlas Icon
*****
Posts: 14,899
Finland


Show only this user's posts in this thread
« Reply #15 on: November 10, 2009, 09:45:37 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it? Smiley

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis Smiley

Still, 0.9999999... is not equal to 1.  Tongue

(1/3)=0.333333333....

(2/3)=0.666666666....

(3/3)=0.999999999....


Gotta wonder whether that excellent public school education you kept telling me about is to blame for an 18-year-old being ignorant of a basic mathematical fact...
Logged
k-onmmunist
Winston Disraeli
Atlas Icon
*****
Posts: 11,753
Palestinian Territory, Occupied


Show only this user's posts in this thread
« Reply #16 on: November 10, 2009, 10:04:58 AM »

I was always taught to regard it as 1.
Logged
Filuwaúrdjan
Realpolitik
Atlas Institution
*****
Posts: 67,609
United Kingdom


Show only this user's posts in this thread
« Reply #17 on: November 10, 2009, 10:14:43 AM »

numbers.

do. not. like.

do. no. want.

go away. numbers.
Logged
Associate Justice PiT
PiT (The Physicist)
Atlas Politician
Atlas Superstar
*****
Posts: 31,135
United States


Show only this user's posts in this thread
« Reply #18 on: November 10, 2009, 10:23:18 AM »

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it? Smiley

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis Smiley

     It all goes back to Zeno's paradox, really. Achilles races with a tortoise. Achilles starts at point A while the tortoise starts at a point B further ahead. By the time he reaches point B, the tortoise has reached point C. By the time Achilles reaches point C, the tortoise has reached point D, & so forth. The implication is that Achilles never reaches the tortoise, but we know that would be false. As such, we realize that at x=infinity, the graph of f(x) = 1/x2 does in fact equal 0. I find limits to be rather fascinating, really. Smiley
Logged
they don't love you like i love you
BRTD
Atlas Prophet
*****
Posts: 112,693
Ukraine


Political Matrix
E: -6.50, S: -6.67

P P
Show only this user's posts in this thread
« Reply #19 on: November 10, 2009, 11:30:17 AM »

What does 1-0.999999.... equal if not zero?

You can't say a number with an infinite number of zeroes between the decimal point and a one, because infinite means without end. So nothing can come after the zeroes.
Logged
Aizen
YaBB God
*****
Posts: 4,511


Political Matrix
E: -3.23, S: -9.22

Show only this user's posts in this thread
« Reply #20 on: November 10, 2009, 12:32:30 PM »

nope. i once did this on a math quiz. if the answer was 28 i would put 27.999999~ and i got it wrong. since i got it wrong and failed the math quiz because i made all my answers like that, it must not be true.
Logged
Antonio the Sixth
Antonio V
Atlas Institution
*****
Posts: 57,959
United States


Political Matrix
E: -7.87, S: -3.83

P P
Show only this user's posts in this thread
« Reply #21 on: November 10, 2009, 12:54:24 PM »

0.9=1

I assumed that was the meaning of the question.
Logged
k-onmmunist
Winston Disraeli
Atlas Icon
*****
Posts: 11,753
Palestinian Territory, Occupied


Show only this user's posts in this thread
« Reply #22 on: November 10, 2009, 02:38:24 PM »


The meaning was 0.9999999∞ being the same as 1, which it is for all purposes, given that it is just 0.000000....1 from it.
Logged
muon2
Moderators
Atlas Icon
*****
Posts: 16,787


Show only this user's posts in this thread
« Reply #23 on: November 10, 2009, 03:23:02 PM »

One area of discrepancy is that the symbol "1" can be used in different contexts. jmfcst's example of its use in floating point arithmetic is one such example. But even in abstract mathematics it can have different meanings.

As a real number the symbol 1 refers to the number that can be represented by any convergent sequence that becomes arbitrarily close to that specified value. Decimal numbers are one form of describing a convergent sequence of a sum of fractions:

1.000... = 1/1 + 0/10 + 0/100 + 0/1000 + ...
0.999... = 0/1 + 9/10 + 9/100 + 9/1000 + ...

Since these sequential sums converge to the same value they represent the same real number. Other sequential sums also represent the real number 1:

1/2 + 1/4 + 1/8 + 1/16 + ...
4/5 + 4/25 + 4/125 + 4/625 + ...

And all these sequences are equal as real numbers.

However, the symbol 1 can also refer to the integer 1, which it might be if use for instance as the simplest counting number. In that case decimal or other fractional sequences can not equate to 1, since they are not themselves only integers. The statement 1 (integer) = 0.999... (real) is either confusing or meaningless since the two sides of the equation are different entities.

When a question like the one for this thread is posted, I assume that the questioner intends for the equals sign to be sensible and relate two items of the same sort. Therefore I answered yes, but I recognize that there is ambiguity in the use of the symbol 1.
Logged
titaniumtux
Rookie
**
Posts: 206
Vatican City State


Political Matrix
E: 9.10, S: -5.13

Show only this user's posts in this thread
« Reply #24 on: November 10, 2009, 04:33:03 PM »


Epic math fail. Three divided by three is one. Ridiculous to suggest that three thirds is anything but one...srsly...
Logged
Pages: [1] 2 3 4  
« previous next »
Jump to:  


Login with username, password and session length

Terms of Service - DMCA Agent and Policy - Privacy Policy and Cookies

Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Page created in 0.072 seconds with 15 queries.